Abstract

We present a theory for polyelectrolytegels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gelelasticity,free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolytegels in salt-free solvents,solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Received 26 October 2011Accepted 12 March 2012Published online 02 April 2012

Acknowledgments:

Acknowledgment is made to the National Institutes of Health (Grant No. R01HG002776), National Science Foundation (Grant No. 0706454), AFOSR (Grant No. FA9550-07-1-0347), and the Materials Research Science and Engineering Center at the University of Massachusetts Amherst. J.H. would like to acknowledge useful discussions with Arindam Kundagrami.